{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Protein folding process analysis with MSM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, we demonstrate how to use the HTMD code for analysing a protein folding process, in this case, of the protein Villin.\n",
    "\n",
    "To analyze, one needs MD trajectories first, which can be generated with HTMD. Here, we already provide the trajectories (data) to analyze. You can download the data from [here](http://pub.htmd.org/tutorials/protein-folding-analysis/datasets.tar.gz) (**Warning: 3GB filesize**)\n",
    "\n",
    "Alternatively, you can download the dataset using `wget`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "assert os.system('wget -rcN -np -nH -q --cut-dirs=2 -R index.html* http://pub.htmd.org/tutorials/protein-folding-analysis/datasets/') == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Getting started"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we import the modules we are going to need for the tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "\n",
      "Please cite HTMD: Doerr et al.(2016)JCTC,12,1845. \n",
      "https://dx.doi.org/10.1021/acs.jctc.6b00049\n",
      "Documentation: http://software.acellera.com/\n",
      "To update: conda update htmd -c acellera -c psi4\n",
      "\n",
      "You are on the latest HTMD version (unpackaged : /home/joao/maindisk/software/repos/Acellera/htmd/htmd).\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from htmd.ui import *\n",
    "config(viewer='webgl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Creating a simulation list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of an analysis, full atom information is required by HTMD. Therefore each simulation trajectory has to be associated with a corresponding PDB file. Additionally, if you plan to run adaptive, each trajectory needs to be associated with an input directory which contains the files used to run the simulations. The simList function allows us to make these associations\n",
    "\n",
    "    sims = simlist(glob('data/*/'), glob('input/*/structure.pdb'), glob('input/*/'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Filtering trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically waters are removed from the trajectories as they are not used in the analysis and it helps speed up further calculations. These filtered trajectories are written into a new directory. The advantage of filtering is that if your input structures only differ in the number of water molecules, you can produce a single unique pdb file for all simulations once you remove the waters, which will speed up calculations. This step is not necessary for the analysis and you can skip it if you don't mind the slowdown in calculations. In that case replace in the following commands the fsims variable with sims.\n",
    "\n",
    "    fsims = simfilter(sims, './filtered/', filtersel='not water')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In this tutorial, in order for the trajectories to be downloaded in a timely manner, we provide only the filtered trajectories which are stored in three separate dataset folders. Therefore we will skip the above two commands and construct the simulation list directly from the filtered trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Creating simlist: 100%|██████████| 708/708 [00:00<00:00, 3765.24it/s]\n",
      "Creating simlist: 100%|██████████| 710/710 [00:00<00:00, 3582.33it/s]\n",
      "Creating simlist: 100%|██████████| 719/719 [00:00<00:00, 3835.12it/s]\n"
     ]
    }
   ],
   "source": [
    "sets = glob('datasets/*/')\n",
    "sims = []\n",
    "for s in sets:\n",
    "    fsims = simlist(glob(s + '/filtered/*/'), 'datasets/1/filtered/filtered.pdb')\n",
    "    sims = simmerge(sims, fsims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calculating metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To build a Markov state model we need to project the atom coordinates onto a lower dimensional space which can be used for clustering the conformations into a set of states. Here we have selected to use the carbon alpha atoms of the protein. This will calculate contacts between all carbon alpha atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Projecting trajectories: 100%|██████████| 2137/2137 [00:18<00:00, 117.61it/s]\n",
      "2018-03-20 00:19:18,232 - htmd.projections.metric - INFO - Frame step 0.10000000149011612ns was read from the trajectories. If it looks wrong, redefine it by manually setting the MetricData.fstep property.\n"
     ]
    }
   ],
   "source": [
    "metr = Metric(sims)\n",
    "metr.set(MetricSelfDistance('protein and name CA', metric='contacts'))\n",
    "data = metr.project()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we provide the frame-step in nanoseconds i.e. the time that passes between two consecutive frames in a trajectory. This is automatically read from the trajectories, however not all trajectories contain the correct fstep so it can be useful to manually define it like here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.fstep = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Removing trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes the set of trajectories can contain trajectories of incorrect length. These are typically corrupted trajectories and are removed.\n",
    "\n",
    "The `plotTrajSizes` method plots all trajectory lengths sorted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plotTrajSizes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`dropTraj` has multiple options for removing simulations from the dataset. Here we use it to remove all trajectories whose length is not equal to the mode length. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-20 00:19:26,084 - htmd.metricdata - INFO - Dropped 7 trajectories from 2137 resulting in 2130\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 168,  472,  709, 1507, 1601, 2100, 2111])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dropTraj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## TICA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TICA is a method that can be used to improve the clustering of the conformations. This is done by projecting the data onto a lower-dimensional space which separates well the metastable minima and places clusters on the transition regions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3397d8e2c8de45c6b488b64321f885b2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/pyemma/__init__.py:91: UserWarning: You are not using the latest release of PyEMMA. Latest is 2.5.1, you have 2.4.\n",
      "  .format(latest=latest, current=current), category=UserWarning)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "df6a771cde6948478a3c9a387c60d36b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tica = TICA(data, 2, units='ns')\n",
    "dataTica = tica.project(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bootstrapping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to bootstrap our calculations we can at this point drop a random 20% of the trajectories and do the rest of the analysis multiple times to see if the results are consistent. Alternatively we can keep on using dataTica in the following commands. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataBoot = dataTica.bootstrap(0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Clustering conformations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have cleaned the dataset we proceed to cluster the conformations.\n",
    "\n",
    "Here we use the mini-batch kmeans clustering algorithm to produce 1000 clusters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataBoot.cluster(MiniBatchKMeans(n_clusters=1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Building the Markov model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "After clustering it is time to build the Markov model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model(dataBoot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before constructing the Markov model we need to choose the lag-time at which it will be built. The lag-time is typically chosen by looking at the implied timescale (ITS) plot and selecting a lag-time at which the top timescales start converging. By constructing Markov models at various lag times HTMD creates a plot which shows the slowest implied timescales of each Markov model at various lag times. If a model is Markovian at a specific lag time, the implied timescales should stay unchanged for any higher lag times. Therefore, given an implied timescales plot, the user can monitor the convergence and choose the lag time at which to construct his Markov model, typically the Markov time which is the shortest lag time at which the timescales converge. Too large lag times can reduce the temporal resolution of the Markov model and can create more statistical uncertainty due to fewer transition counts and thus instability in the implied timescales. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "052d7b2fda1c44f195ceff488998683c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20-03-18 00:30:28 pyemma.msm.estimators.implied_timescales.ImpliedTimescales[2] WARNING  Some timescales could not be computed. Timescales array is smaller than expected or contains NaNs\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-20 00:30:28,228 - pyemma.msm.estimators.implied_timescales.ImpliedTimescales[2] - WARNING - Some timescales could not be computed. Timescales array is smaller than expected or contains NaNs\n",
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/matplotlib/scale.py:114: RuntimeWarning: invalid value encountered in less_equal\n",
      "  out[a <= 0] = -1000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotTimescales()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After seeing the ITS plot we decide on a lag-time of 25ns. Additionally the ITS plot showed us that there is a separation between 3 slow timescales and the rest of the timescales which are fast. Therefore we choose to lump our microstates together into 4 macrostates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-20 00:35:11,623 - htmd.model - INFO - 100.0% of the data was used\n",
      "2018-03-20 00:35:11,744 - htmd.model - INFO - Number of trajectories that visited each macrostate:\n",
      "2018-03-20 00:35:11,745 - htmd.model - INFO - [ 133 1650  559   97]\n"
     ]
    }
   ],
   "source": [
    "model.markovModel(25, 4, units='ns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can also visualize the equilibrium populations of each macrostate using the following command"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.00373013,  0.66425711,  0.11840471,  0.21360806])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.eqDistribution()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Once we have a Markov model we can plot the free energy surface by projecting it on any of our projected coordinates. For example to plot it on the first two TICA coordinates we call it like this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/software/repos/Acellera/htmd/htmd/metricdata.py:786: MatplotlibDeprecationWarning: The griddata function was deprecated in version 2.2.\n",
      "  zi = griddata(x, y, z, xi, yi, interp='linear')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotFES(0, 1, temperature=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can also plot the micro and macrostates on top of the FES by setting `states=True`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/software/repos/Acellera/htmd/htmd/metricdata.py:786: MatplotlibDeprecationWarning: The griddata function was deprecated in version 2.2.\n",
      "  zi = griddata(x, y, z, xi, yi, interp='linear')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotFES(0, 1, temperature=360, states=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Visualizing the states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see what the states look like we can use the `viewStates` method. We load the macrostates and add a protein representation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Getting state Molecules: 100%|██████████| 4/4 [00:08<00:00,  2.03s/it]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7fffab523e7448ab35589b769e5bda4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8a5c1c56335c48529afb7f9f1e363c79",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.viewStates(protein=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calculating the kinetics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the major advantages of Markov state models is that they can provide quantitative results about the kinetics between states.\n",
    "\n",
    "Provide the Kinetics constructor with the system temperature. It automatically then calculates the source and sink states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-20 00:36:47,599 - htmd.kinetics - INFO - Detecting source state...\n",
      "2018-03-20 00:36:49,155 - htmd.kinetics - INFO - Guessing the source state as the state with minimum contacts.\n",
      "2018-03-20 00:36:49,157 - htmd.kinetics - INFO - Source macro = 1\n",
      "2018-03-20 00:36:49,158 - htmd.kinetics - INFO - Detecting sink state...\n",
      "2018-03-20 00:36:49,189 - htmd.kinetics - INFO - Sink macro = 3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "kin = Kinetics(model, temperature=360)\n",
    "print(kin.source)\n",
    "print(kin.sink)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To see the rates between the source and sink states we use the `getRates` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-20 00:37:08,689 - htmd.kinetics - INFO - Calculating rates between source: [1] and sink: [3] states.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mfpton = 1.81E+03 (ns)\n",
      "mfptoff = 2.28E+02 (ns)\n",
      "kon = 5.54E+05 (1/M 1/s)\n",
      "koff = 4.40E+06 (1/s)\n",
      "koff/kon = 7.94E+00 (M)\n",
      "kdeq = 3.11E+00 (M)\n",
      "g0eq = 0.81 (kcal/M)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r = kin.getRates()\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To plot the free energies and mean first passage times of all state use the `plotRates()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ylnVJkqZr3cW0C9g82ZBkDbAduATYBGxNsglYDzw8ftvXGtclSZqiaUBU1R3A4wuaLwAOVNVDVfU0cCNwOTDPKCSa1yVJmq6PMYh1PHulAKNguBB4O/COJJcCexfbOck2YNt484kkD7Yq9ESWN3EG8FjfdQyYn99R8t/g0TnKz++fz/KmPgIiHW1VVU8CPz1t56raAexY8apWmST7q2qu7zqGys/v6PkZHp1j8fn10ZUzD5w1sb0eeKSHOiRJS+gjIO4Czk1ydpJTgCuBPT3UIUlaQutprruBO4HzkswnuaaqngGuA24FHgBuqqr7WtahTnbTHR0/v6PnZ3h0mn9+qarW55AkDZDTSSVJnQyIVWiRO9k1g8VWB9BskpyV5LYkDyS5L8nr+q5pSJI8L8n/SvLZ8ef3+qbns4tpdRnfyf6/gR9lNKPsLmBrVd3fa2EDkeSHgCeA36uqF/Vdz9AkeSHwwqr6VJJvAO4GXu6/v9kkCXBqVT2R5GTgY8DrquoTLc7nFcTqs9id7JrBIqsDaEZV9VdV9anx868ymqiyrt+qhqNGnhhvnjx+NPsr34BYfbruZPc/qI65JBuB7wE+2W8lw5JkTZLPAAeBD1dVs8/PgFh9Ou9kP+ZVaFVL8gLgZuDnquorfdczJFX1tao6n9FNxhckadbVaUCsPt7Jrl6N+85vBt5TVbf0Xc9QVdWXgdtZsGL2SjIgVh/vZFdvxoOs7wYeqKq39l3P0CQ5M8np4+fPBy4G/rzV+QyIVcY72Y9O1+oAfdc0MC8BXgX8SJLPjB8/3ndRA/JC4LYk9zD6Y+/DVfVHrU7mNFdJUievICRJnQwISVInA0KS1MmAkCR1MiAkSZ0MCJ3wklSS35/YPinJo0maTQ9copaLkvzASr1PasmA0GrwJPCi8Y1FMFrJ9osrceDx6rjLcREwyy/+Wd8nNWNAaLX4Y+DS8fOtwO7DLyS5IMmfJfn0+Od54/Y1Sd6S5HNJ7knymnH755P85yQfA/5dkvOTfGL8nj9M8o3j9702yf3j9hvHi9O9Gvj58Q1iL02yJcknx+f+kyT/bJH3nZnk5iR3jR8vGZ/jhyduOPv0eAltaWVUlQ8fJ/SD0fc3fDfwfuB5wGcY/YX+R+PXTwNOGj+/GLh5/PxnGa0ZdPi1bxr//DzwSxPHvwf44fHz3wD+6/j5I8Bzx89PH//8deAXJvb9Rp69YfU/Av9lkff9d+AHx883MFqqAmAv8JLx8xccrtWHj5V4nLQSISMd76rqnvFf5luBfQteXgvckORcRivbnjxuvxh4V42WJ6GqJr8H4r0ASdYy+uX/0XH7DcD7xs/vAd6T5APABxYpbT3w3vEX6ZwC/MUi77sY2DRaygiA08ZXCx8H3prkPcAtVTW/yP7SstnFpNVkD/AWJrqXxt4A3Fajb4jbwugqA0ZLoy+2Fs2TM5zvUmA78L3A3Um6/iD7b8A7qupfAv9p4twLPQd4cVWdP36sq6qvVtUbGV15PB/4RJLvnKEuaSYGhFaTncBvVNXnFrSv5dlB66sn2j8EvPrwL/Yk37TwgFV1CPjbJC8dN70K+GiS5wBnVdVtwC8BpzPqAvoqMDlOMHnuqybaF77vQ4wWWWRcy/njn99eVZ+rqjcB+wEDQivGgNCqUVXzVfXbHS+9GfjNJB8HJmcl/Q7wBeCeJJ8FXrHIoa8Cfmu8wub5jMYh1gB/kORzwKeBt9Vo/f69wL89PPjMaKzhfUn+FHhs4pgL3/daYG484H0/o0FsgJ9Lcu+4vqcYDcZLK8LVXCVJnbyCkCR1MiAkSZ0MCElSJwNCktTJgJAkdTIgJEmdDAhJUicDQpLU6f8DWkswakCRsDMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kin.plotRates()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To visualize the kinetic flux pathways between the source and sink states, use the `plotFluxPathways` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/pyemma/plots/networks.py:544: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if state_labels == 'auto':\n",
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Path flux\t\t%path\t%of total\tpath\n",
      "5.8777605420020455e-05\t100.0%\t100.0%\t\t[1 3]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kin.plotFluxPathways()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And this concludes the protein folding tutorial."
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
